Rovers looked to be on their way to a rare defeat by Burnley but Dunn's 96th minute strike ensured the big match ended 1-1 at Ewood Park.
"In any other game with Dunn having played three games in a week we'd have been looking to get some fresh legs on," Appleton told Radio Rovers after the match.
"But because it was Burnley I kept him on the field, I just knew from an adrenalin point of view that he would keep going until the end.
"I'm delighted for Dunny, he's had a bad time of it with injuries. Dunny is similar to myself, when knocked you tend to come out fighting and he did that today."
Rovers had started brightly but it was the visitors who took the lead just past the half hour. Burnley captain Jason Shackell following up his header that struck the post to fire into an empty net.
"To concede the goal that we did was hugely frustrating as it was another set-play," added Appleton.
"That gave them a lift in the first half and they got into the game a little bit and we had to make sure that we stayed solid and strong."
When Burnley saw Ben Mee sent off for two yellow cards that swung the impetus back in Rovers' favour, and, eventually, they made it count.
"We kept our discipline and they didn't and I think that was the key," continued the Rovers boss.
"It was important that we stayed patient, we worked the ball into the wide areas and we got the reward we deserved.
"The players could have given up, since the Arsenal game everything has gone against us. So for them to pull that out of the bag, and it was richly deserved, I'm delighted.
"So many times we have conceded goals late in games, so it was nice for us to score one for a change.
"It felt like a victory, we should have had a victory."